Meeeh. You can't have more digits than the universe has particles. After all, every digit is stored in one way or another - be it with electrons or ink or anything. The largest number which can be possibly displayed is ultimately tied to the number of stuff in the universe.
That is a problem that isn't actually a problem. In practice, your calendar is bound by the medium you are using to track it. The whole Y2K bollocks was a great example. If you only assign two digits for the "year" variable, you'll run into trouble in less than a hundred years. However, if the upper limit is high enough, for example the number of particles in the universe, you will never ever run into a situation where that would be the bottleneck stopping you from recording more years. Estimating the amount of particles in the universe is more or less flat out impossible, but Answers.com gives a guess that it could be somewhere around 10^82. If we are storing our integer in binary, by placing particles in a row so that each particle is either a one or a zero, we get an upper bound of 2^(10^82). In base ten, this is about 10^(10^81.5). When the Sun is extinguished in five billion years or so, you will have 10^(10^81.5) particles left. This number is so preposterously large that even waiting for the heat death of the universe will not dent it.
Well, if you stored the date in base one, by tossing particles into a bag so that every particle was a single year, you'd only have 10^82 years to work with, which would be considerably less. Still plenty, though.
Ooh! If you used an EXPONENTIAL calendar, so that first you mark down one year, wait two years for the next mark, and four for the next, and store the number in binary, you'd get 2^(2^(10^82)). Of course, you'd need some way to measure the time between marked years, which could become an issue.
I seem to have kind of strayed away from the point I was trying to make. The point I was trying to make was that you only need to be capable of displaying numbers for as long as there exists some entity capable of observing the numbers. When the heat death of the universe rolls around, and the universe is a dark, dissipating cloud of dead stars, it doesn't really matter whether your chosen calendar system is still capable of displaying the year.
I guess this kind of ties back to the doomsday predictions. By the time the Gregorian calendar runs out of space to show the numbers, the world will probably have ended.
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Topic: 2012 (Read 3592 times)